What is included with this book?
Introduction and Preface | p. xi |
Probability | p. 1 |
Probabilities and Events | p. 1 |
Conditional Probability | p. 5 |
Random Variables and Expected Values | p. 9 |
Covariance and Correlation | p. 14 |
Conditional Expectation | p. 16 |
Exercises | p. 17 |
Normal Random Variables | p. 22 |
Continuous Random Variables | p. 22 |
Normal Random Variables | p. 22 |
Properties of Normal Random Variables | p. 26 |
The Central Limit Theorem | p. 29 |
Exercises | p. 31 |
Brownian Motion and Geometric Brownian Motion | p. 34 |
Brownian Motion | p. 34 |
Brownian Motion as a Limit of Simpler Models | p. 35 |
Geometric Brownian Motion | p. 38 |
Geometric Brownian Motion as a Limit of Simpler Models | p. 40 |
*The Maximum Variable | p. 40 |
The Cameron-Martin Theorem | p. 45 |
Exercises | p. 46 |
Interest Rates and Present Value Analysis | p. 48 |
Interest Rates | p. 48 |
Present Value Analysis | p. 52 |
Rate of Return | p. 62 |
Continuously Varying Interest Rates | p. 65 |
Exercises | p. 67 |
Pricing Contracts via Arbitrage | p. 73 |
An Example in Options Pricing | p. 73 |
Other Examples of Pricing via Arbitrage | p. 77 |
Exercises | p. 86 |
The Arbitrage Theorem | p. 92 |
The Arbitrage Theorem | p. 92 |
The Multiperiod Binomial Model | p. 96 |
Proof of the Arbitrage Theorem | p. 98 |
Exercises | p. 102 |
The Black-Scholes Formula | p. 106 |
Introduction | p. 106 |
The Black-Scholes Formula | p. 106 |
Properties of the Black-Scholes Option Cost | p. 110 |
The Delta Hedging Arbitrage Strategy | p. 113 |
Some Derivations | p. 118 |
The Black-Scholes Formula | p. 119 |
The Partial Derivatives | p. 121 |
European Put Options | p. 126 |
Exercises | p. 127 |
Additional Results on Options | p. 131 |
Introduction | p. 131 |
Call Options on Dividend-Paying Securities | p. 131 |
The Dividend for Each Share of the Security Is Paid Continuously in Time at a Rate Equal to a Fixed Fraction f of the Price of the Security | p. 132 |
For Each Share Owned, a Single Payment of fS(td) Is Made at Time td | p. 133 |
For Each Share Owned, a Fixed Amount D Is to Be Paid at Time td | p. 134 |
Pricing American Put Options | p. 134 |
Adding Jumps to Geometric Brownian Motion | p. 142 |
When the Jump Distribution Is Lognormal | p. 144 |
When the Jump Distribution Is General | p. 146 |
Estimating the Volatility Parameter | p. 148 |
Estimating a Population Mean and Variance | p. 149 |
The Standard Estimator of Volatility | p. 150 |
Using Opening and Closing Data | p. 152 |
Using Opening, Closing, and High-Low Data | p. 153 |
Some Comments | p. 155 |
When the Option Cost Differs from the Black-Scholes Formula | p. 155 |
When the Interest Rate Changes | p. 156 |
Final Comments | p. 156 |
Appendix | p. 158 |
Exercises | p. 159 |
Valuing by Expected Utility | p. 165 |
Limitations of Arbitrage Pricing | p. 165 |
Valuing Investments by Expected Utility | p. 166 |
The Portfolio Selection Problem | p. 174 |
Estimating Covariances | p. 184 |
Value at Risk and Conditional Value at Risk | p. 184 |
The Capital Assets Pricing Model | p. 187 |
Rates of Return: Single-Period and Geometric Brownian Motion | p. 188 |
Exercises | p. 190 |
Stochastic Order Relations | p. 193 |
First-Order Stochastic Dominance | p. 193 |
Using Coupling to Show Stochastic Dominance | p. 196 |
Likelihood Ratio Ordering | p. 198 |
A Single-Period Investment Problem | p. 199 |
Second-Order Dominance | p. 203 |
Normal Random Variables | p. 204 |
More on Second-Order Dominance | p. 207 |
Exercises | p. 210 |
Optimization Models | p. 212 |
Introduction | p. 212 |
A Deterministic Optimization Model | p. 212 |
A General Solution Technique Based on Dynamic Programming | p. 213 |
A Solution Technique for Concave Return Functions | p. 215 |
The Knapsack Problem | p. 219 |
Probabilistic Optimization Problems | p. 221 |
A Gambling Model with Unknown Win Probabilities | p. 221 |
An Investment Allocation Model | p. 222 |
Exercises | p. 225 |
Stochastic Dynamic Programming | p. 228 |
The Stochastic Dynamic Programming Problem | p. 228 |
Infinite Time Models | p. 234 |
Optimal Stopping Problems | p. 239 |
Exercises | p. 244 |
Exotic Options | p. 247 |
Introduction | p. 247 |
Barrier Options | p. 247 |
Asian and Lookback Options | p. 248 |
Monte Carlo Simulation | p. 249 |
Pricing Exotic Options by Simulation | p. 250 |
More Efficient Simulation Estimators | p. 252 |
Control and Antithetic Variables in the Simulation of Asian and Lookback Option Valuations | p. 253 |
Combining Conditional Expectation and Importance Sampling in the Simulation of Barrier Option Valuations | p. 257 |
Options with Nonlinear Payoffs | p. 258 |
Pricing Approximations via Multiperiod Binomial Models | p. 259 |
Continuous Time Approximations of Barrier and Lookback Options | p. 261 |
Exercises | p. 262 |
Beyond Geometric Brownian Motion Models | p. 265 |
Introduction | p. 265 |
Crude Oil Data | p. 266 |
Models for the Crude Oil Data | p. 272 |
Final Comments | p. 274 |
Autoregressive Models and Mean Reversion | p. 285 |
The Autoregressive Model | p. 285 |
Valuing Options by Their Expected Return | p. 286 |
Mean Reversion | p. 289 |
Exercises | p. 291 |
Index | p. 303 |
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